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We consider two types of CRIs. The first one is based on quantiles. The second one is the highest
posterior density (HPD) interval.
An f(1 �� ) 100g% quantile-based, or also known as an equal-tailed CRI, is defined as
(q=2; q1��=2), where qa denotes the ath quantile of the posterior distribution. A commonly reported
equal-tailed CRI is (q0:025; q0:975).
HPD interval is defined as an f(1 �� ) 100g% CRI of the shortest width. As its name implies,
this interval corresponds to the region of the posterior density with the highest concentration. For a
unimodal posterior distribution, HPD is unique, but for a multimodal distribution it may not be unique.
Computational approaches for calculating HPD are described in Chen and Shao (1999) and Eberly
and Casella (2003).

Advantages and disadvantages of Bayesian analysis
Bayesian analysis is a powerful analytical tool for statistical modeling, interpretation of results,
and prediction of data. It can be used when there are no standard frequentist methods available or
the existing frequentist methods fail. However, one should be aware of both the advantages and
disadvantages of Bayesian analysis before applying it to a specific problem.
The universality of the Bayesian approach is probably its main methodological advantage to the
traditional frequentist approach. Bayesian inference is based on a single rule of probability, the Bayes
rule, which is applied to all parametric models. This makes the Bayesian approach universal and
greatly facilitates its application and interpretation. The frequentist approach, however, relies on a
variety of estimation methods designed for specific statistical problems and models. Often, inferential
methods designed for one class of problems cannot be applied to another class of models.

尽管您不需要使用Stata进行编程,
但是它作为一个快速完成矩阵的编程
语言,是Stata功能中不可或缺的一部
分。Mata既是一个操作矩阵的互动环
境,也是一个完整开发环境,可以生
产编译和优化代码。它还包含了一些
功能来处理面板数据、执行真实
或复制的矩阵运算,提供完整的支持
面向对象的编程,并完全兼容Stata。

Multiple datasets in memory in Stata 16
You can now load multiple datasets into memory. You type
. use people
and people.dta is loaded into memory. Next, you type
. frame create counties
. frame counties: use counties
and you have two datasets in memory. people.dta is in the frame named default, and counties.dta is in the frame named counties. Your current frame is still default. Most Stata commands use the data in the current frame. For example, if you typed
. list
then people.dta will be listed. If you typed
. frame counties: list
then counties.dta will be listed. Or you could make counties the current frame by typing
. frame change counties
and list will now list the counties data.
Navigating frames is easy and so is linking them. Imagine that both datasets have a variable named countycode that identifies counties in the same way. Type
. frlink m:1 countycode, frame(counties)
and each person in the default frame is linked to a county in the counties frame. This means you can now use the frget command to copy variables from the counties frame to the current frame. Or you can use the frval() function to directly access the values of variables in the counties frame. For instance, if we have each individual’s income in the default frame and median county income in the counties frame, we can generate a new variable containing relative income by typing
. generate rel_income = income / frval(counties, median_income)
This is the beginning. While this example uses only two frames, you can have up to 100 frames in memory at once, and you can have many links among those frames.
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